All companies that fly transport category aircraft utilize QRH procedures. I think the original question pertains to which ones use QRC (Quick Reference Checklists) in lieu of more traditional memory items for all emergencies.

One of the first things I did at my current job was implement a QRC (we're part 91, so it wasn't a big deal). That replaced 14 memory item procedures with just 5 (and 3 of them are "Oxygen mask- Don, Crew communications- Establish).